The universal bilinear construction: bilinear maps V × W → X are in bijection with linear maps V ⊗ W → X. Substrate for multilinear algebra, differential geometry, and deep-learning tensor shapes.
Tensor product V ⊗ W
Related concepts
- Vector space
- Exterior algebra Λ(V)
- Exterior power Λ^k V
- Tensor algebra T(V)
- Quantum entanglement
- Pauli exclusion principle
- Einstein field equations
- Cauchy stress tensor
- Generalised Hooke's law
- Tensor analysis on manifolds
- Density operator ρ: tr ρ = 1, ρ ≽ 0; pure ⇔ ρ² = ρ ⇔ tr ρ² = 1
- Bell states {|Φ±⟩, |Ψ±⟩}: maximally-entangled 2-qubit basis
- No-cloning: ⟨φ|ψ⟩ = √2/2 forbids perfect copy; BH fidelity 5/6, shortfall 1/6